Question

A fire insurance company wants to see if the amount of fire damage (y) in major residential fires is related to the distance between the residence and the nearest fire station (x). The study is to be conducted in a large suburb of a major city, a sample of 15 recent fires in this suburb is selected. The 15 values and the printout follow: A) State the Null and Alternative Hypotheses. In Excel B) Construct a scatter diagram for the data; add a linear trend line to the scatter diagram. C) Run the appropriate test at the 5% significance level to see if there is a relationship between cost of damage and the distance to the nearest fire station. Choose cell C22 for your output. D) Highlight the p-value & make a decision based on the results of your test. What does this mean in this case?

Case	Distance to Fire Station	Amount of damage ($)
1	3.4	26.2
2	1.8	17.8
3	4.6	31.3
4	2.3	23.1
5	3.1	27.5
6	5.5	36.0
7	0.7	14.1
8	3.0	22.3
9	2.6	19.6
10	4.3	31.3
11	2.1	24.0
12	1.1	17.3
13	6.1	43.2
14	4.8	36.4
15	3.8	26.1

Answer 1

Regression analysis is SUMMARY OUTPUT Regression Statistics Multiple R 0.960978 R Square 0.923478 Adjusted R Square 0.917592 Standard Error 2.316346 Observations 15 ANOVA df SS MS F significance F 1 841.7664 841.766 156.8862 0.0000 13 69.75098 5.36546 Regression Residual Total p-value 14 911.5173 Coefficientsandard Err t Stat P-value Lower 95%Upper 95% Intercept 10.27793 1.420278 7.236562 6.59E-06 7.209605 13.34625 Distance to fire stattior 4.919331 0.392748 12.52542 1.25E-08 4.070851 5.767811

Distance Amount to fire of stattion damage 3,4 26,2 Case a) 1 Test hypothesis are H0: B1 = 0 Ha: B1 #0 2 1.8 17.8 3 4,6 31.3 4 2.3 23,1 b) Scattred diagram is with linear trend line 3,1 27.5 5 6 5,5 36 50 45 7 8 0,7 3 2.6 y= 4,9193w + 10.27 ༢=09235 40 14.1 22.3 13.6 31.3 24 35 10 43 2.1 30 11 12 Series1 1.1 17.3 25 13 43.2 20 - Linear (Series1) 6,1 4.8 14 36,4 5 15 3.8 26.1 10 5 0 0 2 4 5 8

c) Test hypothesis are Ho: B1 = 0 H: B1 #0 Test statistic F = 156.886 df1 = 1, df2 = 13 d) p-value =FDIST(156.886,1 13) = 0.0000 Since p-value < 0.05 hence reject the null hypothesis There is suficient evidence to conclude that there is linear relation ship between the cost of damage and the distance to the nearest fire station